15 Nov 2021
Problem 26
Page 306
Section 4.6: Optimization Problems
Chapter 4: Applications of Differentiation
Textbook ExpertVerified Tutor
15 Nov 2021
Given information
A fence 
tall runs parallel to a tall building at a distance of 
from the building.
Step-by-step explanation
Step 1.
According to the question, we can draw a diagram of a fence tall runs parallel to a tall building at a distance of from the building.
From the figure we see that we have a right triangle involving the hypotenuse labeled by r, which represents the length of the ladder. So from the Pythagorean Theorem we have the equation
We also have similar right triangles, one with vertical side 
, the height of the fence, and the other with vertical side 
feet, where indicates how far up the building the ladder touches. Using the fact that ratios of sides for similar triangles are equal we have
, the height of the fence, and the other with vertical side feet, where indicates how far up the building the ladder touches. Using the fact that ratios of sides for similar triangles are equal we have
Single Variable Calculus: Early Transcendentals
4th Edition, 2018
Stewart
ISBN: 9781337687805
Solutions
Chapter
Section
- Problem 1a
- Problem 1b
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